source('../env.R')
community_data = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'community_assembly_metrics_using_relative_abundance.csv'))
Rows: 336 Columns: 43── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
dbl (43): mntd_normalised, mntd_actual, mntd_min, mntd_max, mntd_mean, mntd_sd, fdiv_normalised, fdiv_actual, fdiv_min, fdiv_max, fdiv_mean, fdiv_sd, mass_fdi...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(community_data)
colnames(community_data)
 [1] "mntd_normalised"                  "mntd_actual"                      "mntd_min"                         "mntd_max"                        
 [5] "mntd_mean"                        "mntd_sd"                          "fdiv_normalised"                  "fdiv_actual"                     
 [9] "fdiv_min"                         "fdiv_max"                         "fdiv_mean"                        "fdiv_sd"                         
[13] "mass_fdiv_normalised"             "mass_fdiv_actual"                 "mass_fdiv_min"                    "mass_fdiv_max"                   
[17] "mass_fdiv_mean"                   "mass_fdiv_sd"                     "locomotory_trait_fdiv_normalised" "locomotory_trait_fdiv_actual"    
[21] "locomotory_trait_fdiv_min"        "locomotory_trait_fdiv_max"        "locomotory_trait_fdiv_mean"       "locomotory_trait_fdiv_sd"        
[25] "trophic_trait_fdiv_normalised"    "trophic_trait_fdiv_actual"        "trophic_trait_fdiv_min"           "trophic_trait_fdiv_max"          
[29] "trophic_trait_fdiv_mean"          "trophic_trait_fdiv_sd"            "gape_width_fdiv_normalised"       "gape_width_fdiv_actual"          
[33] "gape_width_fdiv_min"              "gape_width_fdiv_max"              "gape_width_fdiv_mean"             "gape_width_fdiv_sd"              
[37] "handwing_index_fdiv_normalised"   "handwing_index_fdiv_actual"       "handwing_index_fdiv_min"          "handwing_index_fdiv_max"         
[41] "handwing_index_fdiv_mean"         "handwing_index_fdiv_sd"           "city_id"                         

Join on realms

city_to_realm = read_csv(filename(CITY_DATA_OUTPUT_DIR, 'realms.csv'))
Rows: 337 Columns: 2── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): core_realm
dbl (1): city_id
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
community_data_with_realm = left_join(community_data, city_to_realm)
Joining with `by = join_by(city_id)`

Cities as points

city_points = st_centroid(read_sf(filename(CITY_DATA_OUTPUT_DIR, 'city_selection.shp'))) %>% left_join(community_data_with_realm)
Warning: st_centroid assumes attributes are constant over geometriesWarning: st_centroid does not give correct centroids for longitude/latitude dataJoining with `by = join_by(city_id)`
city_points_coords = st_coordinates(city_points)
city_points$latitude = city_points_coords[,1]
city_points$longitude = city_points_coords[,2]
world_map = read_country_boundaries()
Reading layer `WB_countries_Admin0_10m' from data source `/Users/james/Dropbox/PhD/WorldBank_countries_Admin0_10m/WB_countries_Admin0_10m.shp' using driver `ESRI Shapefile'
Simple feature collection with 251 features and 52 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -180 ymin: -59.47275 xmax: 180 ymax: 83.6341
Geodetic CRS:  WGS 84
Warning: st_simplify does not correctly simplify longitude/latitude data, dTolerance needs to be in decimal degrees

Load community data, and create long format version

communities = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'communities_for_analysis.csv'))
Rows: 2427 Columns: 12── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (5): city_name, jetz_species_name, seasonal, presence, origin
dbl (4): city_id, distance_to_northern_edge_km, distance_to_southern_edge_km, relative_abundance_proxy
lgl (3): present_urban_high, present_urban_med, present_urban_low
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
communities
community_summary = communities %>% group_by(city_id) %>% summarise(regional_pool_size = n(), urban_pool_size = sum(relative_abundance_proxy > 0))
community_summary

Load trait data

traits = read_csv(filename(TAXONOMY_OUTPUT_DIR, 'traits_jetz.csv'))
Rows: 304 Columns: 6── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): jetz_species_name
dbl (5): gape_width, trophic_trait, locomotory_trait, mass, handwing_index
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(traits)

Load realm geo

resolve = read_resolve()
head(resolve)
Simple feature collection with 6 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -162.1547 ymin: -69.55876 xmax: 158.6167 ymax: 61.53428
Geodetic CRS:  WGS 84

Summary metrics by Realm

test_required_values = function(name, df) {
  cat(paste(
    test_value_wilcox(paste(name, 'MNTD'), df$mntd_normalised),
    test_value_wilcox(paste(name, 'Beak Gape FDiv'), df$gape_width_fdiv_normalised),
    test_value_wilcox(paste(name, 'HWI FDiv'), df$handwing_index_fdiv_normalised),
    test_value_wilcox(paste(name, 'Mass FDiv'), df$mass_fdiv_normalised),
    nrow(df),
    sep = "\n"))
}
test_required_values('Global', community_data_with_realm)
Global MNTD median 0.49 
Global Beak Gape FDiv median 0.59 ***
Global HWI FDiv median 0.66 ***
Global Mass FDiv median 0.65 ***
336
unique(community_data_with_realm$core_realm)
[1] "Oceania"     "Nearctic"    "Neotropic"   "Palearctic"  "Afrotropic"  "Indomalayan" "Australasia"
test_required_values('Nearctic', community_data_with_realm[community_data_with_realm$core_realm == 'Nearctic',])
Warning: cannot compute exact p-value with tiesWarning: cannot compute exact p-value with ties
Nearctic MNTD median 0.65 
Nearctic Beak Gape FDiv median 0.63 
Nearctic HWI FDiv median 0.23 **
Nearctic Mass FDiv median 0.48 
66
test_required_values('Neotropic', community_data_with_realm[community_data_with_realm$core_realm == 'Neotropic',])
Neotropic MNTD median 0.5 
Neotropic Beak Gape FDiv median 0.47 
Neotropic HWI FDiv median 0.52 
Neotropic Mass FDiv median 0.66 ***
64
test_required_values('Palearctic', community_data_with_realm[community_data_with_realm$core_realm == 'Palearctic',])
Palearctic MNTD median 0.59 *
Palearctic Beak Gape FDiv median 0.93 ***
Palearctic HWI FDiv median 0.4 
Palearctic Mass FDiv median 0.55 
74
test_required_values('Afrotropic', community_data_with_realm[community_data_with_realm$core_realm == 'Afrotropic',])
Afrotropic MNTD median 0.16 *
Afrotropic Beak Gape FDiv median 0.42 
Afrotropic HWI FDiv median 0.54 
Afrotropic Mass FDiv median 0.34 
9
test_required_values('Indomalayan', community_data_with_realm[community_data_with_realm$core_realm == 'Indomalayan',])
Indomalayan MNTD median 0.44 ***
Indomalayan Beak Gape FDiv median 0.46 
Indomalayan HWI FDiv median 0.88 ***
Indomalayan Mass FDiv median 0.8 ***
116
test_required_values('Australasia', community_data_with_realm[community_data_with_realm$core_realm == 'Australasia',])
Australasia MNTD median 0.53 
Australasia Beak Gape FDiv median 0.46 
Australasia HWI FDiv median 0.78 
Australasia Mass FDiv median 0.55 
6

What families exist in which realms?

communities %>% 
  left_join(city_to_realm) %>% 
  mutate(family = gsub( "_.*$", "", jetz_species_name)) %>%
  dplyr::select(family, core_realm) %>%
  distinct() %>%
  arrange(core_realm)
Joining with `by = join_by(city_id)`

Summary metrics by introduced species

communities = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'communities_for_analysis.csv'))
Rows: 2427 Columns: 12── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (5): city_name, jetz_species_name, seasonal, presence, origin
dbl (4): city_id, distance_to_northern_edge_km, distance_to_southern_edge_km, relative_abundance_proxy
lgl (3): present_urban_high, present_urban_med, present_urban_low
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
city_introduced_species = communities %>% group_by(city_id) %>% summarise(number_of_species = n()) %>% left_join(
  communities %>% group_by(city_id) %>% filter(origin == 'Introduced') %>% summarise(number_of_introduced_species = n())
) %>% replace_na(list(number_of_introduced_species = 0))
Joining with `by = join_by(city_id)`
community_data_with_introductions = left_join(community_data, city_introduced_species)
Joining with `by = join_by(city_id)`
community_data_with_introductions$has_introduced_species = community_data_with_introductions$number_of_introduced_species > 0
community_data_with_introductions
community_data_with_introductions[,c('mntd_normalised', 'has_introduced_species')]
community_data_with_introductions %>% group_by(has_introduced_species) %>% summarise(
  total_cities = n(), 
  
  mean_mntd_normalised = mean(mntd_normalised, na.rm = T),
  median_mntd_normalised = median(mntd_normalised, na.rm = T),
  sd_mntd_normalised = sd(mntd_normalised, na.rm = T),
  
  mean_mass_fdiv_normalised = mean(mass_fdiv_normalised, na.rm = T),
  median_mass_fdiv_normalised = median(mass_fdiv_normalised, na.rm = T),
  sd_mass_fdiv_normalised = sd(mass_fdiv_normalised, na.rm = T),
  
  mean_gape_width_fdiv_normalised = mean(gape_width_fdiv_normalised, na.rm = T),
  median_gape_width_fdiv_normalised = median(gape_width_fdiv_normalised, na.rm = T),
  sd_gape_width_fdiv_normalised = sd(gape_width_fdiv_normalised, na.rm = T),
  
  mean_handwing_index_fdiv_normalised = mean(handwing_index_fdiv_normalised, na.rm = T),
  median_handwing_index_fdiv_normalised = median(handwing_index_fdiv_normalised, na.rm = T),
  sd_handwing_index_fdiv_normalised = sd(handwing_index_fdiv_normalised, na.rm = T)
)

MNTD

ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = mntd_normalised)) + geom_boxplot()

wilcox.test(mntd_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')

    Wilcoxon rank sum test with continuity correction

data:  mntd_normalised by has_introduced_species
W = 10512, p-value = 0.02269
alternative hypothesis: true location shift is not equal to 0

There is a significant difference between the response of cities with introduced species (0.53±0.27) and those without (0.47±0.19) (p-value = 0.02).

Mass FDiv

ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = mass_fdiv_normalised)) + geom_boxplot()

wilcox.test(mass_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')

    Wilcoxon rank sum test with continuity correction

data:  mass_fdiv_normalised by has_introduced_species
W = 16441, p-value = 0.0000002359
alternative hypothesis: true location shift is not equal to 0

There is a significant difference between the response of cities with introduced species (0.57±0.27) and those without (0.73±0.24) (p < 0.0001)

Beak Gape FDiv

ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = gape_width_fdiv_normalised)) + geom_boxplot()

wilcox.test(gape_width_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')

    Wilcoxon rank sum test with continuity correction

data:  gape_width_fdiv_normalised by has_introduced_species
W = 10658, p-value = 0.1538
alternative hypothesis: true location shift is not equal to 0

There is NOT a significant difference between the response of cities with introduced species (0.61±0.30) and those without (0.56±0.27)

HWI FDiv

ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = handwing_index_fdiv_normalised)) + geom_boxplot()

wilcox.test(handwing_index_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')

    Wilcoxon rank sum test with continuity correction

data:  handwing_index_fdiv_normalised by has_introduced_species
W = 18856, p-value < 0.00000000000000022
alternative hypothesis: true location shift is not equal to 0

There is a significant difference between the response of cities with introduced species (0.49±0.30) and those without (0.79±0.21) (p < 0.0001)

Examine individual metrics

Analysis data frame

geography = read_csv(filename(CITY_DATA_OUTPUT_DIR, 'geography.csv'))
Rows: 342 Columns: 26── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
dbl (26): city_id, city_avg_ndvi, city_avg_elevation, city_avg_temp, city_avg_min_monthly_temp, city_avg_max_monthly_temp, city_avg_monthly_temp, city_avg_rai...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
names(geography)
 [1] "city_id"                       "city_avg_ndvi"                 "city_avg_elevation"            "city_avg_temp"                
 [5] "city_avg_min_monthly_temp"     "city_avg_max_monthly_temp"     "city_avg_monthly_temp"         "city_avg_rainfall"            
 [9] "city_avg_max_monthly_rainfall" "city_avg_min_monthly_rainfall" "city_avg_soil_moisture"        "city_max_elev"                
[13] "city_min_elev"                 "city_elev_range"               "region_20km_avg_ndvi"          "region_20km_avg_elevation"    
[17] "region_20km_avg_soil_moisture" "region_20km_max_elev"          "region_20km_min_elev"          "region_20km_elev_range"       
[21] "region_50km_avg_ndvi"          "region_50km_avg_elevation"     "region_50km_avg_soil_moisture" "region_50km_max_elev"         
[25] "region_50km_min_elev"          "region_50km_elev_range"       
analysis_data = community_data_with_realm[,c('city_id', 'mntd_normalised', 'mass_fdiv_normalised', 'gape_width_fdiv_normalised', 'handwing_index_fdiv_normalised', 'core_realm')] %>% 
  left_join(city_points[,c('city_id', 'latitude', 'longitude')]) %>%
  left_join(community_data_with_introductions[,c('city_id', 'has_introduced_species')]) %>%
  left_join(geography)
Joining with `by = join_by(city_id)`Joining with `by = join_by(city_id)`Joining with `by = join_by(city_id)`
analysis_data$abs_latitude = abs(analysis_data$latitude)
analysis_data$core_realm = factor(analysis_data$core_realm, levels = c('Palearctic', 'Nearctic', 'Neotropic', 'Afrotropic', 'Indomalayan', 'Australasia', 'Oceania'))
analysis_data$has_introduced_species = factor(analysis_data$has_introduced_species, level = c('TRUE', 'FALSE'), labels = c('Introduced species', 'No introduced species'))
model_data = function(df, dependant_var) {
  df[,c(dependant_var, 'core_realm', 'abs_latitude', 'latitude', 'longitude', 'has_introduced_species', 'city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range', 'region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 'region_20km_min_elev', 'region_20km_elev_range', 'region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 'region_50km_min_elev', 'region_50km_elev_range')]
}
model_data(analysis_data, 'mntd_normalised')
names(analysis_data)
 [1] "city_id"                        "mntd_normalised"                "mass_fdiv_normalised"           "gape_width_fdiv_normalised"    
 [5] "handwing_index_fdiv_normalised" "core_realm"                     "latitude"                       "longitude"                     
 [9] "geometry"                       "has_introduced_species"         "city_avg_ndvi"                  "city_avg_elevation"            
[13] "city_avg_temp"                  "city_avg_min_monthly_temp"      "city_avg_max_monthly_temp"      "city_avg_monthly_temp"         
[17] "city_avg_rainfall"              "city_avg_max_monthly_rainfall"  "city_avg_min_monthly_rainfall"  "city_avg_soil_moisture"        
[21] "city_max_elev"                  "city_min_elev"                  "city_elev_range"                "region_20km_avg_ndvi"          
[25] "region_20km_avg_elevation"      "region_20km_avg_soil_moisture"  "region_20km_max_elev"           "region_20km_min_elev"          
[29] "region_20km_elev_range"         "region_50km_avg_ndvi"           "region_50km_avg_elevation"      "region_50km_avg_soil_moisture" 
[33] "region_50km_max_elev"           "region_50km_min_elev"           "region_50km_elev_range"         "abs_latitude"                  
all_explanatories = c(
    'abs_latitude', 'latitude', 'longitude', 
    'has_introduced_species',
    'city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 
    'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 
    'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range',
    'region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 
    'region_20km_min_elev', 'region_20km_elev_range',
    'region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 
    'region_50km_min_elev', 'region_50km_elev_range',
    'core_realmAfrotropic', 'core_realmAustralasia', 'core_realmIndomalayan', 'core_realmNearctic', 'core_realmNeotropic', 'core_realmPalearctic')

type_labels = function(p) {
  explanatory_levels = all_explanatories[all_explanatories %in% p$explanatory]
  p$explanatory <- factor(p$explanatory, levels = explanatory_levels)
  
  p$type <- 'Realm'
  p$type[p$explanatory %in% c('city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 
    'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 
    'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range')] <- 'City geography'
  p$type[p$explanatory %in% c('region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 
    'region_50km_min_elev', 'region_50km_elev_range')] <- 'Regional (50km) geography'
   p$type[p$explanatory %in% c('region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 
    'region_20km_min_elev', 'region_20km_elev_range')] <- 'Regional (20km) geography'
  p$type[p$explanatory %in% c('abs_latitude', 'latitude', 'longitude')] <- 'Spatial'
  p
}
explanatory_labels = c(
  'has_introduced_species'='Has introduced species', 
  'city_avg_ndvi'='Average NDVI', 
  'city_avg_elevation'='Average elevation', 
  'city_avg_temp'='Average temperature', 
  'city_avg_min_monthly_temp'='Average minimum monthly temperature', 
  'city_avg_max_monthly_temp'='Average maximum monthly temperature', 
  'city_avg_monthly_temp'='Average monthly temperature', 
  'city_avg_rainfall'='Average rainfall', 
  'city_avg_max_monthly_rainfall'='Average maximum monthly rainfall', 
  'city_avg_min_monthly_rainfall'='Average minimum monthly rainfall', 
  'city_avg_soil_moisture'='Average soil moisture', 
  'city_max_elev'='Maximum elevation', 
  'city_min_elev'='Minimum elevation', 
  'city_elev_range'='Elevation range', 
  'region_20km_avg_ndvi'='Average NDVI', 
  'region_20km_avg_elevation'='Average elevation', 
  'region_20km_avg_soil_moisture'='Average soil moisture', 
  'region_20km_max_elev'='Maximum elevation', 
  'region_20km_min_elev'='Minimum elevation',
  'region_20km_elev_range'='Elevation range',
  'region_50km_avg_ndvi'='Average NDVI',
  'region_50km_avg_elevation'='Average elevation',
  'region_50km_avg_soil_moisture'='Average soil moisture', 
  'region_50km_max_elev'='Maximum elevation',
  'region_50km_min_elev'='Minimum elevation', 
  'region_50km_elev_range'='Elevation range',
  'abs_latitude' = 'Absolute latitude',
  'latitude' = 'Latitude',
  'longitude' = 'Longitude',
  'core_realmAfrotropic' = 'Afrotropical', 
  'core_realmAustralasia' = 'Austaliasian', 
  'core_realmIndomalayan' = 'Indomalayan', 
  'core_realmNearctic' = 'Nearctic', 
  'core_realmNeotropic' = 'Neotropical',
  'core_realmPalearctic' = 'Palearctic',
  'core_realmOceania' = 'Oceanical')

Helper plot functions

geom_normalised_histogram = function(name, gg, legend.position = "bottom") {
  gg + 
    geom_histogram(aes(fill = core_realm), binwidth = 0.1, position = "dodge") +
    geom_vline(aes(xintercept = 0.5), color = "#000000", size = 0.4) +
    geom_vline(aes(xintercept = 0), color = "#000000", size = 0.2, linetype = "dashed") +
    geom_vline(aes(xintercept = 1), color = "#000000", size = 0.2, linetype = "dashed") + 
    ylab("Number of cities") + xlab("Normalised Response") + ylim(c(0, 70)) +
    labs(title = name, fill = 'Realm') +
    theme_bw() +
    theme(legend.position=legend.position)
}
geom_map = function(map_sf, title) {
  norm_mntd_analysis_geo = ggplot() + 
    geom_sf(data = world_map, aes(geometry = geometry)) +
    map_sf +
    normalised_colours_scale +
    labs(colour = 'Normalised\nResponse') +
    theme_bw() +
    theme(legend.position="bottom")
}

Helper Dredge functions

# Taken from MuMIN package
# https://rdrr.io/cran/MuMIn/src/R/averaging.R
# https://rdrr.io/cran/MuMIn/src/R/model.avg.R

.coefarr.avg <-
  function(cfarr, weight, revised.var, full, alpha) {   
    weight <- weight / sum(weight)
    nCoef <- dim(cfarr)[3L]
    if(full) {
      nas <- is.na(cfarr[, 1L, ]) & is.na(cfarr[, 2L, ])
      cfarr[, 1L, ][nas] <- cfarr[, 2L, ][nas] <- 0
      #cfarr[, 1L:2L, ][is.na(cfarr[, 1L:2L, ])] <- 0
      if(!all(is.na(cfarr[, 3L, ])))
        cfarr[ ,3L, ][is.na(cfarr[ , 3L, ])] <- Inf
    }
    
    avgcoef <- array(dim = c(nCoef, 5L),
                     dimnames = list(dimnames(cfarr)[[3L]], c("Estimate",
                                                              "Std. Error", "Adjusted SE", "Lower CI", "Upper CI")))
    for(i in seq_len(nCoef))
      avgcoef[i, ] <- par.avg(cfarr[, 1L, i], cfarr[, 2L, i], weight,
                              df = cfarr[, 3L, i], alpha = alpha, revised.var = revised.var)
    
    avgcoef[is.nan(avgcoef)] <- NA
    return(avgcoef)
  }

.makecoefmat <- function(cf) {
  no.ase <- all(is.na(cf[, 3L]))
  z <- abs(cf[, 1L] / cf[, if(no.ase) 2L else 3L])
  pval <- 2 * pnorm(z, lower.tail = FALSE)
  cbind(cf[, if(no.ase) 1L:2L else 1L:3L, drop = FALSE],
        `z value` = z, `Pr(>|z|)` = zapsmall(pval))
}

# Generate model selections using lmer, dredge, and model.avg
# `forumla` : a two-sided linear formula object describing both the fixed-effects and random-effects part of the model
# `data` : the data frame containing the variables from the formula
# `aic_delta` : the AIC delta to use for selecting models in model average
model_average <- function(formula, data, aic_delta = 20) {
  model <- lm(
    formula,
    data=data
  )
  dredge_result <- dredge(model)
  summary(model.avg(dredge_result, subset = delta < aic_delta))
}

# Create a summary data frame containing the selected variables from a model
# `model_sum` : The model summary output from `model_average`
model_summary <- function(model_sum) {
  .column_name <- function(postfix) {
    postfix
  }
  
  # just return the estimate and p value
  weight <- model_sum$msTable[, 5L]
  
  coefmat.full <- as.data.frame(.makecoefmat(.coefarr.avg(model_sum$coefArray, weight,
                                                          attr(model_sum, "revised.var"), TRUE, 0.05)))
  
  coefmat.subset <-
    as.data.frame(.makecoefmat(.coefarr.avg(model_sum$coefArray, weight,
                                            attr(model_sum, "revised.var"), FALSE, 0.05)))
  
  
  coefmat.subset <- coefmat.subset[-c(1), c(1, 2, 5)]
  names(coefmat.subset) <- c(.column_name("estimate"), .column_name("error"), .column_name("p"))
  coefmat.subset <- tibble::rownames_to_column(coefmat.subset, "explanatory")
  coefmat.subset$model = 'subset'
  
  coefmat.full <- coefmat.full[-c(1), c(1, 2, 5)]
  names(coefmat.full) <- c(.column_name("estimate"), .column_name("error"), .column_name("p"))
  coefmat.full <- tibble::rownames_to_column(coefmat.full, "explanatory")
  coefmat.full$model = 'full'
  
  rbind(coefmat.full, coefmat.subset)
}
formula_from_vsurp = function(predictors, dependent, vsurp_result) {
  as.formula(paste(dependent, paste(names(predictors[,vsurp_result$varselect.interp]), collapse="+"), sep = "~"))
}
plot_vsurp_result = function(result_table) {
  plot = result_table[result_table$model == 'full',]
  plot = type_labels(plot)

  ggplot(plot, aes(y=explanatory, x=estimate, colour = type)) + 
    geom_line() +
    geom_point()+
    geom_errorbar(aes(xmin=estimate-error, xmax=estimate+error), width=.2,
                   position=position_dodge(0.05)) +
    scale_y_discrete(
      limits = rev(levels(plot$explanatory)), 
      labels = explanatory_labels) +
    theme_bw() +
    geom_vline(xintercept=0, linetype="dotted") +
    guides(colour=guide_legend(title="Predictor type")) + xlab('Increase from 0 (habitat filtering)\nto 1 (competitive exclusion)\n± Standard Error') + ylab('Predictor') +
    theme(legend.justification = "top")
}

MNTD

norm_mntd_analysis_plot = geom_normalised_histogram(
  'MNTD', 
  ggplot(analysis_data, aes(mntd_normalised))
)
Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
Please use `linewidth` instead.
norm_mntd_analysis_plot

norm_mntd_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = mntd_normalised, geometry = geometry)), 'MNTD')
norm_mntd_analysis_geo_plot

norm_mntd_analysis_data = model_data(analysis_data[!is.na(analysis_data$mntd_normalised),], 'mntd_normalised')
norm_mntd_analysis_predictors = norm_mntd_analysis_data[,-1]
norm_mntd_analysis_interp = VSURF(x = norm_mntd_analysis_predictors, y = norm_mntd_analysis_data$mntd_normalised)
Thresholding step
Estimated computational time (on one core): 19.5 sec.

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Interpretation step (on 30 variables)
Estimated computational time (on one core): between 7.8 sec. and  37.2 sec.

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Prediction step (on 6 variables)
Maximum estimated computational time (on one core): 2.3 sec.

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names(norm_mntd_analysis_predictors[,norm_mntd_analysis_interp$varselect.interp])
[1] "city_avg_monthly_temp"     "core_realm"                "city_avg_max_monthly_temp" "longitude"                 "city_avg_temp"            
[6] "latitude"                 
norm_mntd_analysis_formula = formula_from_vsurp(norm_mntd_analysis_predictors, "mntd_normalised", norm_mntd_analysis_interp)
norm_mntd_analysis_result <- model_average(norm_mntd_analysis_formula, norm_mntd_analysis_data)
Fixed term is "(Intercept)"
norm_mntd_analysis_result_table = model_summary(norm_mntd_analysis_result)
norm_mntd_analysis_result_table
norm_mntd_analysis_pred_plot = plot_vsurp_result(norm_mntd_analysis_result_table)
norm_mntd_analysis_pred_plot

Gape width - FDiv

norm_gape_fdiv_analysis_plot = geom_normalised_histogram(
  'Gape FDiv', 
  ggplot(analysis_data, aes(gape_width_fdiv_normalised))
)
norm_gape_fdiv_analysis_plot

norm_gape_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = gape_width_fdiv_normalised, geometry = geometry)), 'Gape Width FDiv')
norm_gape_fdiv_analysis_geo_plot

norm_gape_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$gape_width_fdiv_normalised),], 'gape_width_fdiv_normalised')
norm_gape_fdiv_analysis_predictors = norm_gape_fdiv_analysis_data[,-1]
norm_gape_fdiv_analysis_interp = VSURF(x = norm_gape_fdiv_analysis_predictors, y = norm_gape_fdiv_analysis_data$gape_width_fdiv_normalised)
Thresholding step
Estimated computational time (on one core): 16.8 sec.

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Interpretation step (on 30 variables)
Estimated computational time (on one core): between 8.4 sec. and  39 sec.

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Prediction step (on 9 variables)
Maximum estimated computational time (on one core): 4 sec.

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names(norm_gape_fdiv_analysis_predictors[,norm_gape_fdiv_analysis_interp$varselect.interp])
[1] "longitude"                     "core_realm"                    "abs_latitude"                  "city_avg_temp"                
[5] "city_avg_max_monthly_temp"     "city_avg_min_monthly_temp"     "city_avg_max_monthly_rainfall" "latitude"                     
[9] "city_max_elev"                
norm_gape_fdiv_analysis_formula = formula_from_vsurp(norm_gape_fdiv_analysis_predictors, "gape_width_fdiv_normalised", norm_gape_fdiv_analysis_interp)
norm_gape_fdiv_analysis_result <- model_average(norm_gape_fdiv_analysis_formula, norm_gape_fdiv_analysis_data)
Fixed term is "(Intercept)"
norm_gape_fdiv_analysis_result_table = model_summary(norm_gape_fdiv_analysis_result)
norm_gape_fdiv_analysis_result_table
norm_gape_fdiv_analysis_pred_plot = plot_vsurp_result(norm_gape_fdiv_analysis_result_table)
norm_gape_fdiv_analysis_pred_plot

HWI - FDiv

norm_hwi_fdiv_loco_analysis_plot = geom_normalised_histogram(
  'HWI FDiv', 
  ggplot(analysis_data, aes(handwing_index_fdiv_normalised))
)
norm_hwi_fdiv_loco_analysis_plot

norm_hwi_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = handwing_index_fdiv_normalised, geometry = geometry)), 'HWI FDiv')
norm_hwi_fdiv_analysis_geo_plot

norm_hwi_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$handwing_index_fdiv_normalised),], 'handwing_index_fdiv_normalised')
norm_hwi_fdiv_analysis_predictors = norm_hwi_fdiv_analysis_data[,-1]
norm_hwi_fdiv_analysis_interp = VSURF(x = norm_hwi_fdiv_analysis_predictors, y = norm_hwi_fdiv_analysis_data$handwing_index_fdiv_normalised)
Thresholding step
Estimated computational time (on one core): 15.3 sec.

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Interpretation step (on 30 variables)
Estimated computational time (on one core): between 6.6 sec. and  36.3 sec.

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Prediction step (on 7 variables)
Maximum estimated computational time (on one core): 2.3 sec.

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names(norm_hwi_fdiv_analysis_predictors[,norm_hwi_fdiv_analysis_interp$varselect.interp])
[1] "latitude"                      "core_realm"                    "city_avg_max_monthly_temp"     "city_avg_temp"                
[5] "longitude"                     "city_avg_max_monthly_rainfall" "region_50km_min_elev"         
norm_hwi_fdiv_analysis_formula = formula_from_vsurp(norm_hwi_fdiv_analysis_predictors, "handwing_index_fdiv_normalised", norm_hwi_fdiv_analysis_interp)
norm_hwi_fdiv_analysis_result <- model_average(norm_hwi_fdiv_analysis_formula, norm_hwi_fdiv_analysis_data)
Fixed term is "(Intercept)"
norm_hwi_fdiv_analysis_result_table = model_summary(norm_hwi_fdiv_analysis_result)
norm_hwi_fdiv_analysis_result_table
norm_hwi_fdiv_analysis_pred_plot = plot_vsurp_result(norm_hwi_fdiv_analysis_result_table)
norm_hwi_fdiv_analysis_pred_plot

Mass - FDiv

norm_mass_fdiv_loco_analysis_plot = geom_normalised_histogram(
  'Mass FDiv', 
  ggplot(analysis_data, aes(mass_fdiv_normalised))
)
norm_mass_fdiv_loco_analysis_plot

norm_mass_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = mass_fdiv_normalised, geometry = geometry)), 'Mass FDiv')
norm_mass_fdiv_analysis_geo_plot

norm_mass_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$mass_fdiv_normalised),], 'mass_fdiv_normalised')
norm_mass_fdiv_analysis_predictors = norm_mass_fdiv_analysis_data[,-1]
norm_mass_fdiv_analysis_interp = VSURF(x = norm_mass_fdiv_analysis_predictors, y = norm_mass_fdiv_analysis_data$mass_fdiv_normalised)
Thresholding step
Estimated computational time (on one core): 16.6 sec.

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Interpretation step (on 30 variables)
Estimated computational time (on one core): between 1.8 sec. and  34.5 sec.

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Prediction step (on 5 variables)
Maximum estimated computational time (on one core): 0.9 sec.

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names(norm_mass_fdiv_analysis_predictors[,norm_mass_fdiv_analysis_interp$varselect.interp])
[1] "core_realm"                    "abs_latitude"                  "city_avg_temp"                 "latitude"                     
[5] "city_avg_max_monthly_rainfall"
norm_mass_fdiv_analysis_formula = formula_from_vsurp(norm_mass_fdiv_analysis_predictors, "mass_fdiv_normalised", norm_mass_fdiv_analysis_interp)
norm_mass_fdiv_analysis_result <- model_average(norm_mass_fdiv_analysis_formula, norm_mass_fdiv_analysis_data)
Fixed term is "(Intercept)"
norm_mass_fdiv_analysis_result_table = model_summary(norm_mass_fdiv_analysis_result)
norm_mass_fdiv_analysis_result_table
norm_mass_fdiv_analysis_pred_plot = plot_vsurp_result(norm_mass_fdiv_analysis_result_table)
norm_mass_fdiv_analysis_pred_plot

Create plot of differences in process response

pred_legend <- get_legend(
  # create some space to the left of the legend
  norm_hwi_fdiv_analysis_pred_plot + theme(legend.box.margin = margin(0, 0, 0, 12))
)
Warning: Removed 1 row containing missing values or values outside the scale range (`geom_line()`).`geom_line()`: Each group consists of only one observation.
ℹ Do you need to adjust the group aesthetic?Warning: Removed 1 row containing missing values or values outside the scale range (`geom_point()`).Warning: Multiple components found; returning the first one. To return all, use `return_all = TRUE`.
geo_legend <- get_legend(
  # create some space to the left of the legend
  norm_mass_fdiv_analysis_geo_plot + theme(legend.box.margin = margin(0, 0, 0, 12))
)
Warning: Multiple components found; returning the first one. To return all, use `return_all = TRUE`.
plot_grid(
  plot_grid(
    norm_mntd_analysis_geo_plot + theme(legend.position="none"), 
    norm_mntd_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("MNTD", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_gape_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_gape_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("Gape", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_hwi_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_hwi_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("HWI", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_mass_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_mass_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("Mass", size = 16, angle = 90, x = 0.01, y = 0.5), 
  plot_grid(
    geo_legend, 
    pred_legend, 
    nrow = 1
  ),
  nrow = 5
)
`geom_line()`: Each group consists of only one observation.
ℹ Do you need to adjust the group aesthetic?`geom_line()`: Each group consists of only one observation.
ℹ Do you need to adjust the group aesthetic?Warning: Removed 1 row containing missing values or values outside the scale range (`geom_line()`).`geom_line()`: Each group consists of only one observation.
ℹ Do you need to adjust the group aesthetic?Warning: Removed 1 row containing missing values or values outside the scale range (`geom_point()`).Warning: Removed 1 row containing missing values or values outside the scale range (`geom_line()`).`geom_line()`: Each group consists of only one observation.
ℹ Do you need to adjust the group aesthetic?Warning: Removed 1 row containing missing values or values outside the scale range (`geom_point()`).
ggsave(filename(FIGURES_OUTPUT_DIR, 'process_response.jpg'), width = 2500, height=5000, units = 'px')

Compare metrics against each other

ggplot(analysis_data, aes(x = gape_width_fdiv_normalised, y = mntd_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("MNTD") + 
  xlab("Gape Width FDiv") +
  theme_bw() + labs(color = "Realm")

ggplot(analysis_data, aes(x = handwing_index_fdiv_normalised, y = mntd_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("MNTD") + 
  xlab("HWI FDiv") +
  theme_bw() + labs(color = "Realm")

ggplot(analysis_data, aes(x = handwing_index_fdiv_normalised, y = gape_width_fdiv_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("Gape Width FDiv") + 
  xlab("HWI FDiv") +
  theme_bw() + labs(color = "Realm")

mntd_fdiv_analysis = analysis_data %>% 
  dplyr::select(city_id,  mntd_normalised, handwing_index_fdiv_normalised, gape_width_fdiv_normalised) %>%
  left_join(community_summary) %>%
  mutate(urban_pool_perc = urban_pool_size * 100 / regional_pool_size)
Joining with `by = join_by(city_id)`
mntd_fdiv_analysis
ggpairs(mntd_fdiv_analysis %>% dplyr::select(mntd_normalised, handwing_index_fdiv_normalised, gape_width_fdiv_normalised, regional_pool_size, urban_pool_size, urban_pool_perc))
ggsave(filename(FIGURES_OUTPUT_DIR, 'appendix_normalised_correlation.jpg'))
Saving 7.29 x 4.51 in image

---
title: "Metrics for assessing community assembly processes"
output: html_notebook
bibliography: ../ref.bib  
---

```{r}
source('../env.R')
```

```{r}
community_data = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'community_assembly_metrics_using_relative_abundance.csv'))
head(community_data)
colnames(community_data)
```

Join on realms
```{r}
city_to_realm = read_csv(filename(CITY_DATA_OUTPUT_DIR, 'realms.csv'))
community_data_with_realm = left_join(community_data, city_to_realm)
```

Cities as points
```{r}
city_points = st_centroid(read_sf(filename(CITY_DATA_OUTPUT_DIR, 'city_selection.shp'))) %>% left_join(community_data_with_realm)
city_points_coords = st_coordinates(city_points)
city_points$latitude = city_points_coords[,1]
city_points$longitude = city_points_coords[,2]
```
  
```{r}
world_map = read_country_boundaries()
```

Load community data, and create long format version
```{r}
communities = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'communities_for_analysis.csv'))
communities
```

```{r}
community_summary = communities %>% group_by(city_id) %>% summarise(regional_pool_size = n(), urban_pool_size = sum(relative_abundance_proxy > 0))
community_summary
```

Load trait data
```{r}
traits = read_csv(filename(TAXONOMY_OUTPUT_DIR, 'traits_jetz.csv'))
head(traits)
```

Load realm geo
```{r}
resolve = read_resolve()
head(resolve)
```

# Summary metrics by Realm
```{r}
test_required_values = function(name, df) {
  cat(paste(
    test_value_wilcox(paste(name, 'MNTD'), df$mntd_normalised),
    test_value_wilcox(paste(name, 'Beak Gape FDiv'), df$gape_width_fdiv_normalised),
    test_value_wilcox(paste(name, 'HWI FDiv'), df$handwing_index_fdiv_normalised),
    test_value_wilcox(paste(name, 'Mass FDiv'), df$mass_fdiv_normalised),
    nrow(df),
    sep = "\n"))
}
```

```{r}
test_required_values('Global', community_data_with_realm)
```

```{r}
unique(community_data_with_realm$core_realm)
```

```{r}
test_required_values('Nearctic', community_data_with_realm[community_data_with_realm$core_realm == 'Nearctic',])
```

```{r}
test_required_values('Neotropic', community_data_with_realm[community_data_with_realm$core_realm == 'Neotropic',])
```

```{r}
test_required_values('Palearctic', community_data_with_realm[community_data_with_realm$core_realm == 'Palearctic',])
```

```{r}
test_required_values('Afrotropic', community_data_with_realm[community_data_with_realm$core_realm == 'Afrotropic',])
```

```{r}
test_required_values('Indomalayan', community_data_with_realm[community_data_with_realm$core_realm == 'Indomalayan',])
```

```{r}
test_required_values('Australasia', community_data_with_realm[community_data_with_realm$core_realm == 'Australasia',])
```

# What families exist in which realms?
```{r}
communities %>% 
  left_join(city_to_realm) %>% 
  mutate(family = gsub( "_.*$", "", jetz_species_name)) %>%
  dplyr::select(family, core_realm) %>%
  distinct() %>%
  arrange(core_realm)
```

# Summary metrics by introduced species
```{r}
communities = read_csv(filename(COMMUNITY_OUTPUT_DIR, 'communities_for_analysis.csv'))
city_introduced_species = communities %>% group_by(city_id) %>% summarise(number_of_species = n()) %>% left_join(
  communities %>% group_by(city_id) %>% filter(origin == 'Introduced') %>% summarise(number_of_introduced_species = n())
) %>% replace_na(list(number_of_introduced_species = 0))

community_data_with_introductions = left_join(community_data, city_introduced_species)
community_data_with_introductions$has_introduced_species = community_data_with_introductions$number_of_introduced_species > 0
community_data_with_introductions
```

```{r}
community_data_with_introductions[,c('mntd_normalised', 'has_introduced_species')]
```

```{r}
community_data_with_introductions %>% group_by(has_introduced_species) %>% summarise(
  total_cities = n(), 
  
  mean_mntd_normalised = mean(mntd_normalised, na.rm = T),
  median_mntd_normalised = median(mntd_normalised, na.rm = T),
  sd_mntd_normalised = sd(mntd_normalised, na.rm = T),
  
  mean_mass_fdiv_normalised = mean(mass_fdiv_normalised, na.rm = T),
  median_mass_fdiv_normalised = median(mass_fdiv_normalised, na.rm = T),
  sd_mass_fdiv_normalised = sd(mass_fdiv_normalised, na.rm = T),
  
  mean_gape_width_fdiv_normalised = mean(gape_width_fdiv_normalised, na.rm = T),
  median_gape_width_fdiv_normalised = median(gape_width_fdiv_normalised, na.rm = T),
  sd_gape_width_fdiv_normalised = sd(gape_width_fdiv_normalised, na.rm = T),
  
  mean_handwing_index_fdiv_normalised = mean(handwing_index_fdiv_normalised, na.rm = T),
  median_handwing_index_fdiv_normalised = median(handwing_index_fdiv_normalised, na.rm = T),
  sd_handwing_index_fdiv_normalised = sd(handwing_index_fdiv_normalised, na.rm = T)
)
```

## MNTD
```{r}
ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = mntd_normalised)) + geom_boxplot()
```

```{r}
wilcox.test(mntd_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')
```

There is a significant difference between the response of cities with introduced species (0.53±0.27) and those without (0.47±0.19) (p-value = 0.02).


## Mass FDiv
```{r}
ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = mass_fdiv_normalised)) + geom_boxplot()
```

```{r}
wilcox.test(mass_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')
```
There is a significant difference between the response of cities with introduced species (0.57±0.27) and those without (0.73±0.24) (p < 0.0001)


## Beak Gape FDiv
```{r}
ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = gape_width_fdiv_normalised)) + geom_boxplot()
```

```{r}
wilcox.test(gape_width_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')
```
There is NOT a significant difference between the response of cities with introduced species (0.61±0.30) and those without (0.56±0.27)


## HWI FDiv
```{r}
ggplot(community_data_with_introductions, aes(x = has_introduced_species, y = handwing_index_fdiv_normalised)) + geom_boxplot()
```

```{r}
wilcox.test(handwing_index_fdiv_normalised ~ has_introduced_species, community_data_with_introductions, na.action = 'na.omit')
```
There is a significant difference between the response of cities with introduced species (0.49±0.30) and those without (0.79±0.21) (p < 0.0001)


# Examine individual metrics

## Analysis data frame
```{r}
geography = read_csv(filename(CITY_DATA_OUTPUT_DIR, 'geography.csv'))
names(geography)
```

```{r}
analysis_data = community_data_with_realm[,c('city_id', 'mntd_normalised', 'mass_fdiv_normalised', 'gape_width_fdiv_normalised', 'handwing_index_fdiv_normalised', 'core_realm')] %>% 
  left_join(city_points[,c('city_id', 'latitude', 'longitude')]) %>%
  left_join(community_data_with_introductions[,c('city_id', 'has_introduced_species')]) %>%
  left_join(geography)

analysis_data$abs_latitude = abs(analysis_data$latitude)
analysis_data$core_realm = factor(analysis_data$core_realm, levels = c('Palearctic', 'Nearctic', 'Neotropic', 'Afrotropic', 'Indomalayan', 'Australasia', 'Oceania'))
analysis_data$has_introduced_species = factor(analysis_data$has_introduced_species, level = c('TRUE', 'FALSE'), labels = c('Introduced species', 'No introduced species'))
```

```{r}
model_data = function(df, dependant_var) {
  df[,c(dependant_var, 'core_realm', 'abs_latitude', 'latitude', 'longitude', 'has_introduced_species', 'city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range', 'region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 'region_20km_min_elev', 'region_20km_elev_range', 'region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 'region_50km_min_elev', 'region_50km_elev_range')]
}
model_data(analysis_data, 'mntd_normalised')
```

```{r}
names(analysis_data)
```

```{r}
all_explanatories = c(
    'abs_latitude', 'latitude', 'longitude', 
    'has_introduced_species',
    'city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 
    'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 
    'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range',
    'region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 
    'region_20km_min_elev', 'region_20km_elev_range',
    'region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 
    'region_50km_min_elev', 'region_50km_elev_range',
    'core_realmAfrotropic', 'core_realmAustralasia', 'core_realmIndomalayan', 'core_realmNearctic', 'core_realmNeotropic', 'core_realmPalearctic')

type_labels = function(p) {
  explanatory_levels = all_explanatories[all_explanatories %in% p$explanatory]
  p$explanatory <- factor(p$explanatory, levels = explanatory_levels)
  
  p$type <- 'Realm'
  p$type[p$explanatory %in% c('city_avg_ndvi', 'city_avg_elevation', 'city_avg_temp', 'city_avg_min_monthly_temp', 'city_avg_max_monthly_temp', 
    'city_avg_monthly_temp', 'city_avg_rainfall', 'city_avg_max_monthly_rainfall', 'city_avg_min_monthly_rainfall', 
    'city_avg_soil_moisture', 'city_max_elev', 'city_min_elev', 'city_elev_range')] <- 'City geography'
  p$type[p$explanatory %in% c('region_50km_avg_ndvi', 'region_50km_avg_elevation', 'region_50km_avg_soil_moisture', 'region_50km_max_elev', 
    'region_50km_min_elev', 'region_50km_elev_range')] <- 'Regional (50km) geography'
   p$type[p$explanatory %in% c('region_20km_avg_ndvi', 'region_20km_avg_elevation', 'region_20km_avg_soil_moisture', 'region_20km_max_elev', 
    'region_20km_min_elev', 'region_20km_elev_range')] <- 'Regional (20km) geography'
  p$type[p$explanatory %in% c('abs_latitude', 'latitude', 'longitude')] <- 'Spatial'
  p
}
```

```{r}
explanatory_labels = c(
  'has_introduced_species'='Has introduced species', 
  'city_avg_ndvi'='Average NDVI', 
  'city_avg_elevation'='Average elevation', 
  'city_avg_temp'='Average temperature', 
  'city_avg_min_monthly_temp'='Average minimum monthly temperature', 
  'city_avg_max_monthly_temp'='Average maximum monthly temperature', 
  'city_avg_monthly_temp'='Average monthly temperature', 
  'city_avg_rainfall'='Average rainfall', 
  'city_avg_max_monthly_rainfall'='Average maximum monthly rainfall', 
  'city_avg_min_monthly_rainfall'='Average minimum monthly rainfall', 
  'city_avg_soil_moisture'='Average soil moisture', 
  'city_max_elev'='Maximum elevation', 
  'city_min_elev'='Minimum elevation', 
  'city_elev_range'='Elevation range', 
  'region_20km_avg_ndvi'='Average NDVI', 
  'region_20km_avg_elevation'='Average elevation', 
  'region_20km_avg_soil_moisture'='Average soil moisture', 
  'region_20km_max_elev'='Maximum elevation', 
  'region_20km_min_elev'='Minimum elevation',
  'region_20km_elev_range'='Elevation range',
  'region_50km_avg_ndvi'='Average NDVI',
  'region_50km_avg_elevation'='Average elevation',
  'region_50km_avg_soil_moisture'='Average soil moisture', 
  'region_50km_max_elev'='Maximum elevation',
  'region_50km_min_elev'='Minimum elevation', 
  'region_50km_elev_range'='Elevation range',
  'abs_latitude' = 'Absolute latitude',
  'latitude' = 'Latitude',
  'longitude' = 'Longitude',
  'core_realmAfrotropic' = 'Afrotropical', 
  'core_realmAustralasia' = 'Austaliasian', 
  'core_realmIndomalayan' = 'Indomalayan', 
  'core_realmNearctic' = 'Nearctic', 
  'core_realmNeotropic' = 'Neotropical',
  'core_realmPalearctic' = 'Palearctic',
  'core_realmOceania' = 'Oceanical')
```

## Helper plot functions
```{r}
geom_normalised_histogram = function(name, gg, legend.position = "bottom") {
  gg + 
    geom_histogram(aes(fill = core_realm), binwidth = 0.1, position = "dodge") +
    geom_vline(aes(xintercept = 0.5), color = "#000000", size = 0.4) +
    geom_vline(aes(xintercept = 0), color = "#000000", size = 0.2, linetype = "dashed") +
    geom_vline(aes(xintercept = 1), color = "#000000", size = 0.2, linetype = "dashed") + 
    ylab("Number of cities") + xlab("Normalised Response") + ylim(c(0, 70)) +
    labs(title = name, fill = 'Realm') +
    theme_bw() +
    theme(legend.position=legend.position)
}
```

```{r}
geom_map = function(map_sf, title) {
  norm_mntd_analysis_geo = ggplot() + 
    geom_sf(data = world_map, aes(geometry = geometry)) +
    map_sf +
    normalised_colours_scale +
    labs(colour = 'Normalised\nResponse') +
    theme_bw() +
    theme(legend.position="bottom")
}
```

## Helper Dredge functions
```{r}
# Taken from MuMIN package
# https://rdrr.io/cran/MuMIn/src/R/averaging.R
# https://rdrr.io/cran/MuMIn/src/R/model.avg.R

.coefarr.avg <-
  function(cfarr, weight, revised.var, full, alpha) {	
    weight <- weight / sum(weight)
    nCoef <- dim(cfarr)[3L]
    if(full) {
      nas <- is.na(cfarr[, 1L, ]) & is.na(cfarr[, 2L, ])
      cfarr[, 1L, ][nas] <- cfarr[, 2L, ][nas] <- 0
      #cfarr[, 1L:2L, ][is.na(cfarr[, 1L:2L, ])] <- 0
      if(!all(is.na(cfarr[, 3L, ])))
        cfarr[ ,3L, ][is.na(cfarr[ , 3L, ])] <- Inf
    }
    
    avgcoef <- array(dim = c(nCoef, 5L),
                     dimnames = list(dimnames(cfarr)[[3L]], c("Estimate",
                                                              "Std. Error", "Adjusted SE", "Lower CI", "Upper CI")))
    for(i in seq_len(nCoef))
      avgcoef[i, ] <- par.avg(cfarr[, 1L, i], cfarr[, 2L, i], weight,
                              df = cfarr[, 3L, i], alpha = alpha, revised.var = revised.var)
    
    avgcoef[is.nan(avgcoef)] <- NA
    return(avgcoef)
  }

.makecoefmat <- function(cf) {
  no.ase <- all(is.na(cf[, 3L]))
  z <- abs(cf[, 1L] / cf[, if(no.ase) 2L else 3L])
  pval <- 2 * pnorm(z, lower.tail = FALSE)
  cbind(cf[, if(no.ase) 1L:2L else 1L:3L, drop = FALSE],
        `z value` = z, `Pr(>|z|)` = zapsmall(pval))
}

# Generate model selections using lmer, dredge, and model.avg
# `forumla` : a two-sided linear formula object describing both the fixed-effects and random-effects part of the model
# `data` : the data frame containing the variables from the formula
# `aic_delta` : the AIC delta to use for selecting models in model average
model_average <- function(formula, data, aic_delta = 20) {
  model <- lm(
    formula,
    data=data
  )
  dredge_result <- dredge(model)
  summary(model.avg(dredge_result, subset = delta < aic_delta))
}

# Create a summary data frame containing the selected variables from a model
# `model_sum` : The model summary output from `model_average`
model_summary <- function(model_sum) {
  .column_name <- function(postfix) {
    postfix
  }
  
  # just return the estimate and p value
  weight <- model_sum$msTable[, 5L]
  
  coefmat.full <- as.data.frame(.makecoefmat(.coefarr.avg(model_sum$coefArray, weight,
                                                          attr(model_sum, "revised.var"), TRUE, 0.05)))
  
  coefmat.subset <-
    as.data.frame(.makecoefmat(.coefarr.avg(model_sum$coefArray, weight,
                                            attr(model_sum, "revised.var"), FALSE, 0.05)))
  
  
  coefmat.subset <- coefmat.subset[-c(1), c(1, 2, 5)]
  names(coefmat.subset) <- c(.column_name("estimate"), .column_name("error"), .column_name("p"))
  coefmat.subset <- tibble::rownames_to_column(coefmat.subset, "explanatory")
  coefmat.subset$model = 'subset'
  
  coefmat.full <- coefmat.full[-c(1), c(1, 2, 5)]
  names(coefmat.full) <- c(.column_name("estimate"), .column_name("error"), .column_name("p"))
  coefmat.full <- tibble::rownames_to_column(coefmat.full, "explanatory")
  coefmat.full$model = 'full'
  
  rbind(coefmat.full, coefmat.subset)
}
```

```{r}
formula_from_vsurp = function(predictors, dependent, vsurp_result) {
  as.formula(paste(dependent, paste(names(predictors[,vsurp_result$varselect.interp]), collapse="+"), sep = "~"))
}
```

```{r}
plot_vsurp_result = function(result_table) {
  plot = result_table[result_table$model == 'full',]
  plot = type_labels(plot)

  ggplot(plot, aes(y=explanatory, x=estimate, colour = type)) + 
    geom_line() +
    geom_point()+
    geom_errorbar(aes(xmin=estimate-error, xmax=estimate+error), width=.2,
                   position=position_dodge(0.05)) +
    scale_y_discrete(
      limits = rev(levels(plot$explanatory)), 
      labels = explanatory_labels) +
    theme_bw() +
    geom_vline(xintercept=0, linetype="dotted") +
    guides(colour=guide_legend(title="Predictor type")) + xlab('Increase from 0 (habitat filtering)\nto 1 (competitive exclusion)\n± Standard Error') + ylab('Predictor') +
    theme(legend.justification = "top")
}
```

## MNTD
```{r}
norm_mntd_analysis_plot = geom_normalised_histogram(
  'MNTD', 
  ggplot(analysis_data, aes(mntd_normalised))
)
norm_mntd_analysis_plot
```

```{r}
norm_mntd_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = mntd_normalised, geometry = geometry)), 'MNTD')
norm_mntd_analysis_geo_plot
```

```{r}
norm_mntd_analysis_data = model_data(analysis_data[!is.na(analysis_data$mntd_normalised),], 'mntd_normalised')
norm_mntd_analysis_predictors = norm_mntd_analysis_data[,-1]
norm_mntd_analysis_interp = VSURF(x = norm_mntd_analysis_predictors, y = norm_mntd_analysis_data$mntd_normalised)
names(norm_mntd_analysis_predictors[,norm_mntd_analysis_interp$varselect.interp])
```

```{r}
norm_mntd_analysis_formula = formula_from_vsurp(norm_mntd_analysis_predictors, "mntd_normalised", norm_mntd_analysis_interp)
norm_mntd_analysis_result <- model_average(norm_mntd_analysis_formula, norm_mntd_analysis_data)
norm_mntd_analysis_result_table = model_summary(norm_mntd_analysis_result)
norm_mntd_analysis_result_table
```

```{r}
norm_mntd_analysis_pred_plot = plot_vsurp_result(norm_mntd_analysis_result_table)
norm_mntd_analysis_pred_plot
```

## Gape width - FDiv
```{r}
norm_gape_fdiv_analysis_plot = geom_normalised_histogram(
  'Gape FDiv', 
  ggplot(analysis_data, aes(gape_width_fdiv_normalised))
)
norm_gape_fdiv_analysis_plot
```

```{r}
norm_gape_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = gape_width_fdiv_normalised, geometry = geometry)), 'Gape Width FDiv')
norm_gape_fdiv_analysis_geo_plot
```

```{r}
norm_gape_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$gape_width_fdiv_normalised),], 'gape_width_fdiv_normalised')
norm_gape_fdiv_analysis_predictors = norm_gape_fdiv_analysis_data[,-1]
norm_gape_fdiv_analysis_interp = VSURF(x = norm_gape_fdiv_analysis_predictors, y = norm_gape_fdiv_analysis_data$gape_width_fdiv_normalised)
names(norm_gape_fdiv_analysis_predictors[,norm_gape_fdiv_analysis_interp$varselect.interp])
```

```{r}
norm_gape_fdiv_analysis_formula = formula_from_vsurp(norm_gape_fdiv_analysis_predictors, "gape_width_fdiv_normalised", norm_gape_fdiv_analysis_interp)
norm_gape_fdiv_analysis_result <- model_average(norm_gape_fdiv_analysis_formula, norm_gape_fdiv_analysis_data)
norm_gape_fdiv_analysis_result_table = model_summary(norm_gape_fdiv_analysis_result)
norm_gape_fdiv_analysis_result_table
```

```{r}
norm_gape_fdiv_analysis_pred_plot = plot_vsurp_result(norm_gape_fdiv_analysis_result_table)
norm_gape_fdiv_analysis_pred_plot
```


## HWI - FDiv
```{r}
norm_hwi_fdiv_loco_analysis_plot = geom_normalised_histogram(
  'HWI FDiv', 
  ggplot(analysis_data, aes(handwing_index_fdiv_normalised))
)
norm_hwi_fdiv_loco_analysis_plot
```

```{r}
norm_hwi_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = handwing_index_fdiv_normalised, geometry = geometry)), 'HWI FDiv')
norm_hwi_fdiv_analysis_geo_plot
```

```{r}
norm_hwi_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$handwing_index_fdiv_normalised),], 'handwing_index_fdiv_normalised')
norm_hwi_fdiv_analysis_predictors = norm_hwi_fdiv_analysis_data[,-1]
norm_hwi_fdiv_analysis_interp = VSURF(x = norm_hwi_fdiv_analysis_predictors, y = norm_hwi_fdiv_analysis_data$handwing_index_fdiv_normalised)
names(norm_hwi_fdiv_analysis_predictors[,norm_hwi_fdiv_analysis_interp$varselect.interp])
```


```{r}
norm_hwi_fdiv_analysis_formula = formula_from_vsurp(norm_hwi_fdiv_analysis_predictors, "handwing_index_fdiv_normalised", norm_hwi_fdiv_analysis_interp)
norm_hwi_fdiv_analysis_result <- model_average(norm_hwi_fdiv_analysis_formula, norm_hwi_fdiv_analysis_data)
norm_hwi_fdiv_analysis_result_table = model_summary(norm_hwi_fdiv_analysis_result)
norm_hwi_fdiv_analysis_result_table
```

```{r}
norm_hwi_fdiv_analysis_pred_plot = plot_vsurp_result(norm_hwi_fdiv_analysis_result_table)
norm_hwi_fdiv_analysis_pred_plot
```


## Mass - FDiv
```{r}
norm_mass_fdiv_loco_analysis_plot = geom_normalised_histogram(
  'Mass FDiv', 
  ggplot(analysis_data, aes(mass_fdiv_normalised))
)
norm_mass_fdiv_loco_analysis_plot
```

```{r}
norm_mass_fdiv_analysis_geo_plot = geom_map(geom_sf(data = analysis_data, aes(color = mass_fdiv_normalised, geometry = geometry)), 'Mass FDiv')
norm_mass_fdiv_analysis_geo_plot
```

```{r}
norm_mass_fdiv_analysis_data = model_data(analysis_data[!is.na(analysis_data$mass_fdiv_normalised),], 'mass_fdiv_normalised')
norm_mass_fdiv_analysis_predictors = norm_mass_fdiv_analysis_data[,-1]
norm_mass_fdiv_analysis_interp = VSURF(x = norm_mass_fdiv_analysis_predictors, y = norm_mass_fdiv_analysis_data$mass_fdiv_normalised)
names(norm_mass_fdiv_analysis_predictors[,norm_mass_fdiv_analysis_interp$varselect.interp])
```

```{r}
norm_mass_fdiv_analysis_formula = formula_from_vsurp(norm_mass_fdiv_analysis_predictors, "mass_fdiv_normalised", norm_mass_fdiv_analysis_interp)
norm_mass_fdiv_analysis_result <- model_average(norm_mass_fdiv_analysis_formula, norm_mass_fdiv_analysis_data)
norm_mass_fdiv_analysis_result_table = model_summary(norm_mass_fdiv_analysis_result)
norm_mass_fdiv_analysis_result_table
```

```{r}
norm_mass_fdiv_analysis_pred_plot = plot_vsurp_result(norm_mass_fdiv_analysis_result_table)
norm_mass_fdiv_analysis_pred_plot
```

# Create plot of differences in process response
```{r}
pred_legend <- get_legend(
  # create some space to the left of the legend
  norm_hwi_fdiv_analysis_pred_plot + theme(legend.box.margin = margin(0, 0, 0, 12))
)
geo_legend <- get_legend(
  # create some space to the left of the legend
  norm_mass_fdiv_analysis_geo_plot + theme(legend.box.margin = margin(0, 0, 0, 12))
)

plot_grid(
  plot_grid(
    norm_mntd_analysis_geo_plot + theme(legend.position="none"), 
    norm_mntd_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("MNTD", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_gape_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_gape_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("Gape", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_hwi_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_hwi_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("HWI", size = 16, angle = 90, x = 0.01, y = 0.5),
  plot_grid(
    norm_mass_fdiv_analysis_geo_plot + theme(legend.position="none"), 
    norm_mass_fdiv_analysis_pred_plot + theme(legend.position="none"), 
    nrow = 1
  ) + draw_label("Mass", size = 16, angle = 90, x = 0.01, y = 0.5), 
  plot_grid(
    geo_legend, 
    pred_legend, 
    nrow = 1
  ),
  nrow = 5
)
ggsave(filename(FIGURES_OUTPUT_DIR, 'process_response.jpg'), width = 2500, height=5000, units = 'px')
```


# Compare metrics against each other
```{r}
ggplot(analysis_data, aes(x = gape_width_fdiv_normalised, y = mntd_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("MNTD") + 
  xlab("Gape Width FDiv") +
  theme_bw() + labs(color = "Realm")
```

```{r}
ggplot(analysis_data, aes(x = handwing_index_fdiv_normalised, y = mntd_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("MNTD") + 
  xlab("HWI FDiv") +
  theme_bw() + labs(color = "Realm")
```

```{r}
ggplot(analysis_data, aes(x = handwing_index_fdiv_normalised, y = gape_width_fdiv_normalised, colour = core_realm)) + 
  geom_point() +
  ylab("Gape Width FDiv") + 
  xlab("HWI FDiv") +
  theme_bw() + labs(color = "Realm")
```

```{r}
mntd_fdiv_analysis = analysis_data %>% 
  dplyr::select(city_id,  mntd_normalised, handwing_index_fdiv_normalised, gape_width_fdiv_normalised) %>%
  left_join(community_summary) %>%
  mutate(urban_pool_perc = urban_pool_size * 100 / regional_pool_size)
mntd_fdiv_analysis
```

```{r}
ggpairs(mntd_fdiv_analysis %>% dplyr::select(mntd_normalised, handwing_index_fdiv_normalised, gape_width_fdiv_normalised, regional_pool_size, urban_pool_size, urban_pool_perc))
ggsave(filename(FIGURES_OUTPUT_DIR, 'appendix_normalised_correlation.jpg'))
```


